why is this

sujoy

Junior Member
Joined
Apr 30, 2005
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110
Hi…i
There is a problem & I have solved it too however with one method things work out & with the other I am basically getting confused, could you please explain the facts
Ques] find the no., of two digit nos., where the product of the nos., is more than the sum of the nos.
Solution] we negate the statement such a*b< = a+b # if we are able to solve this then the
complement of this gives the answer => a*b-a-b+1 < = 1 => a[b-1]-1[b-1] < =1
so, a =1 or b =1 or a=b-=2 or b= 0 thus from 11 to 19 we get 9 nos{when a =1}&when b=1 ,from 21 to 91 we get 8 nos& when b=0 we get 10 to90 {9 nos}& 22 { 1 number}
so the no of 2 digits is 90-27=63 [ adding all we get 27]
however
if we do a*b> a+b then we get a[b-1]-1[b-1]>1……=>[a-1][b-1] >1
WHY IS THIS APPARENT CONTRADICTION…..could you ALSO give me the name of chapter I should read to get these concepts more cleared
REGARDS
sujoy
 
sujoy said:
could you ALSO give me the name of chapter I should read
:shock: How could we possibly know what book(s) you might be using, that we could tell you the chapter(s) to read?

Eliz.
 
Why is This?

Unless I misinterpreted your question, the following 2 digit numbers satisfy your requirement

23 - 29
32 - 39
42 - 49
52 - 59
62 - 69
72 - 79
82 - 89
92 - 99
 
Your question as it is typed:

"find the no., of two digit nos., where the product of the nos., is more than the sum of the nos"

So you MUST mean: where the product of the DIGITS is more....
(once again, sujoy, you commited a blasphemy!)

Look at it this way; if they are equal:
ab = a + b
ab - b = a
b = a / (a - 1)
Only integer solution is a = b = 2

So the digits of the qualifying numbers must add to 5 or more (with no 0 or 1)
(as Teacher William's list indicates!)

Your next question:
"could you ALSO give me the name of chapter I should read to get these concepts more cleared"

I don't know...but I'm sure Eliz can help you with this...:)
 
I don't see a contradiction. If you finish the first you get
(a-1)(b-1)<=1
Negating that gives
(a-1)(b-1)>1,
the same as your second.
And the number of candidates matches Will's list.
Nice work.
---------------
Gene
 
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I want to say *THANK YOU TO EVERYBODY* t'was really of great help
regards
Sujoy
 
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